A public school elite runs this country because Labour and Tory governments destroyed grammar schools

John Major is right. It's shocking that a public school elite runs every single sphere of British influence. But the even more shocking thing is that, not so long ago, it didn't used to be like that.

As I said on the Today Programme this morning – debating the issue with Owen Jones – David Cameron is the first public-school-educated Tory Prime Minister since Alec Douglas-Home, who left power 46 years before Cameron came to office. Tony Blair was the first public-school-educated Labour Prime Minister since Clement Attlee, who also left power 46 years before Blair came to office.

What happened in the interim? Grammar schools were almost completely eradicated by both Tory and Labour governments. In the early 1960s, Oxbridge was largely dominated by those educated at grammar schools; dodgy private schools were on the verge of collapsing, so far behind the grammar schools were they in academic excellence.

But then the grammar schools were largely eradicated, and social mobility, which had been improving, started going into reverse. The thousands of grammar school pupils who would have produced rivals to Cameron, Clegg, Osborne and Boris no longer existed. The last Tory leader to benefit from a grammar school – Michael Howard – had an education as good as he'd have got at any public school. When I went back to his old school, Llanelli Grammar, when he became Tory leader, I found it rather difficult – it had been demolished, to be replaced by a comprehensive.

The guilty men and women who got rid of the grammar schools were a mixed bunch. There was the usual brigade of privately-educated education secretaries who pulled up the drawbridge behind them: Shirley Williams (St Paul's Girls' School and Somerville, Oxford) wanted to eradicate all private schools and grammar schools; Tony Crosland (Highgate and Trinity, Oxford) said he wanted to destroy every "f***ing" grammar school in the country. Tristram Hunt (UCS and Trinity, Cambridge) and Nick Clegg (Westminster and Robinson College, Cambridge) are continuing in the same vein, insisting that free schools must have qualified teachers and follow the national curriculum, when their brilliant schools weren't hamstrung by these government impositions.

I'm afraid the sainted Margaret Thatcher is one of the guilty, too, in closing down grammar schools; as are every Education Secretary and Prime Minister since the 1960s, including John Major, who have failed to reverse the closure of grammar schools.

Michael Gove is the first Education Secretary in half a century who has tried to turn the tide but it's a pretty powerful tide to turn. It's not just the near-abolition of grammar schools that's led to this tragic decline in social mobility. The dumbing down of exams, the removal of O-Levels, the decline in rigour of what is taught and how exams are marked, the priority of thoughts over facts, the fear of difficulty, the fear of history… The list goes on and on.

Gove has done his best to turn the clock back in many of these areas. But, on the big question – the return of grammar schools – he has no chance, as long as the government is in coalition with Nick Clegg, who is so determined to pull the ladder up behind him.

There are lots of other factors behind the creation of a public school elite. Owen Jones – who I agreed with on a lot of things this morning – pointed out the massive gulf between the top and the bottom when it came to the amount of words spoken to middle-class babies, as against working-class ones.

But we couldn't agree about the effectiveness of grammar schools. He made the point that their presence in an area did little to improve the lot of those who didn't get into them. True – and tragic – enough. But the argument still stands – that grammar schools were a ladder of opportunity to bridge the yawning gap between that public school elite and the less fortunate.

Those other huge areas of social inequality – in diet, health, amount of words spoken – are undeniable, too. But they are so deeply embedded and, in the extreme cases, so incurable – you can't force a silent mother to start talking to her baby – that there is no easy solution. Of all these problems, there is one that is immediately curable by government action and, worse, one which was produced by government action. Bring back grammar schools.